Really bright F(ab')2 Fragment antibody with some background staining

I used this antibody to stain human cells that were lentivirally transduced to express a mouse receptor on their cell surface. I also used this to estimate the frequency of cells that successfully incorporated the gene of interest and expressed the encoding protein on their surface. The cells were stained in a 1:250 dilution of the antibody at 4 degrees celcius for 30 minutes and washed before analysis using flow cytometry on the alexa-fluor 647 channel. The figure shows that almost 75% of the cells expressed this receptor. However, even the negative population seems to have shifted around half log in fluorescence suggesting some background staining. I purified the positive population and confirmed expression at a later time. I would recommended a titration of the antibody for first time users.